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NSTX APS DPP 2009 – Kinetic Effects in RWM Stability (Berkery)November 3, 2009 A window of weakened stability can be found between the bounce and precession drift stabilizing resonances What causes this rotation profile to be marginally stable to the RWM? –Examine its relation to bounce and precession drift frequencies. 7 marginally stable profile

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NSTX APS DPP 2009 – Kinetic Effects in RWM Stability (Berkery)November 3, 2009 A window of weakened stability can be found between the bounce and precession drift stabilizing resonances The experimentally marginally stable ω E profile is in- between the stabilizing resonances. –Is this true for each of the widely different unstable profiles? 7

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NSTX APS DPP 2009 – Kinetic Effects in RWM Stability (Berkery)November 3, 2009 The experimentally marginally stable ω E profile is in- between the stabilizing resonances. –Is this true for each of the widely different unstable profiles: Yes 7 A window of weakened stability can be found between the bounce and precession drift stabilizing resonances

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NSTX APS DPP 2009 – Kinetic Effects in RWM Stability (Berkery)November 3, 2009 γ is found with a self-consistent or perturbative approach The self-consistent (MARS) approach: solve for γ and ω from: The perturbative (MISK) approach: solve for γ and ω from: with δW ∞ and δW b from PEST. There are three main differences between the approaches: 1.The way that rational surfaces are treated. 2.Whether ξ is changed or unchanged by kinetic effects. 3.Whether γ and ω are non-linearly included in the calculation.

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NSTX APS DPP 2009 – Kinetic Effects in RWM Stability (Berkery)November 3, 2009 Rational surfaces are treated differently The self-consistent (MARS) approach: solve for γ and ω from: MARS-K: “continuum damping included through MHD terms”. This term includes parallel sound wave damping. In MISK a layer of surfaces at a rational ±Δq is removed from the calculation and treated separately through shear Alfvén damping.

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NSTX APS DPP 2009 – Kinetic Effects in RWM Stability (Berkery)November 3, 2009 δW K in the limit of high particle energy Writing δW K without specifying f: Rewriting with explicit energy dependence: So that, for energetic particles, where ε is very large: large Note: this term is independent of ε.